Exploiting Submodular Value Functions For Scaling Up Active Perception
- URL: http://arxiv.org/abs/2009.09696v1
- Date: Mon, 21 Sep 2020 09:11:36 GMT
- Title: Exploiting Submodular Value Functions For Scaling Up Active Perception
- Authors: Yash Satsangi, Shimon Whiteson, Frans A. Oliehoek, Matthijs T. J.
Spaan
- Abstract summary: In active perception tasks, agent aims to select sensory actions that reduce uncertainty about one or more hidden variables.
Partially observable Markov decision processes (POMDPs) provide a natural model for such problems.
As the number of sensors available to the agent grows, the computational cost of POMDP planning grows exponentially.
- Score: 60.81276437097671
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: In active perception tasks, an agent aims to select sensory actions that
reduce its uncertainty about one or more hidden variables. While partially
observable Markov decision processes (POMDPs) provide a natural model for such
problems, reward functions that directly penalize uncertainty in the agent's
belief can remove the piecewise-linear and convex property of the value
function required by most POMDP planners. Furthermore, as the number of sensors
available to the agent grows, the computational cost of POMDP planning grows
exponentially with it, making POMDP planning infeasible with traditional
methods. In this article, we address a twofold challenge of modeling and
planning for active perception tasks. We show the mathematical equivalence of
$\rho$POMDP and POMDP-IR, two frameworks for modeling active perception tasks,
that restore the PWLC property of the value function. To efficiently plan for
active perception tasks, we identify and exploit the independence properties of
POMDP-IR to reduce the computational cost of solving POMDP-IR (and
$\rho$POMDP). We propose greedy point-based value iteration (PBVI), a new POMDP
planning method that uses greedy maximization to greatly improve scalability in
the action space of an active perception POMDP. Furthermore, we show that,
under certain conditions, including submodularity, the value function computed
using greedy PBVI is guaranteed to have bounded error with respect to the
optimal value function. We establish the conditions under which the value
function of an active perception POMDP is guaranteed to be submodular. Finally,
we present a detailed empirical analysis on a dataset collected from a
multi-camera tracking system employed in a shopping mall. Our method achieves
similar performance to existing methods but at a fraction of the computational
cost leading to better scalability for solving active perception tasks.
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